A new approach to the decomposition of boolean functions. 4. non-disjoint decomposition: the method of p, q-partitions

Authors:
B. Ye. Rytsar
Affiliations:
Rzeszów University, Rzeszów, Poland
Venue:
Cybernetics and Systems Analysis
Year:
2009

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Abstract

A set-theoretical approach to the non-disjoint decomposition of different forms of representation of Boolean functions of n variables is considered. This approach is based on the method of p,q-partitions of conjuncterms and on the concept of a decomposition clone. Two techniques of searching for some non-disjoint functional decomposition are described. Theorems on the non-disjoint decomposition of full and partial functions and their systems are formulated. The proposed approach is illustrated by examples.